A FUZZY LOGIC BASED CONTROLLER FOR AN INDIRECT

VECTOR CONTROLLED THREE-PHASE INDUCTION MOTOR

Norman Mariun, Samsul Bahari Mohd Noor, Jasronita Jasni, Omar S. BennanesDepartment of Electrical and Electronic Engineering,

Faculty of Engineering Universiti Putra Malaysia43400 Serdang, Malaysia

Email : norman@eng.upm.edu.my

ABSTRACT 2. INDIRECT VECTOR CONTROL OF

INDUCTION MOTOR This paper presents the theory, design and simulationof a fuzzy logic based controller used for an indirectvector controlled three-phase induction motor. Theanalysis, design and simulation of the fuzzy logiccontroller for IVCIM drive system are carried outbased on the fuzzy set theory. The FLC algorithm has been simulated on Simulink Toolbox in Matlab. Theperformance of the proposed FLC has beeninvestigated and compared to the results obtainedfrom the conventional PI controller based drive atdifferent operating conditions such as sudden changein load. The simulation results demonstrate that theperformance of the FLC is better than that for theconventional PI controller.

The indirect vector control method is essentially thesame as the direct vector control, except that the rotorangle e is generated in an indirect manner(estimation) using the measured speed r and the slipspeed sl. To implement the indirect vector controlstrategy, it is necessary to take dynamic equation intoconsideration and the following equations (1-5);

slrslree dtdt (1)

For decoupling control, the stator flux componentof current ids should be aligned on the de axis, and thetorque component of current iqs should be on the qe

axis, that leads to and then:0qr rdrKeywords

Induction motor drives, Speed control, Fuzzy Logiccontrollers, Matlab/Simulink software.

dsmrr

r

r iLdt

dRL

(2)1. INTRODUCTION

Induction motors have a simple and rugged structure;moreover, they are economical and immune to heavyoverloads. However the use of induction motors alsohas its disadvantages, mainly the controllability, dueto its complex mathematical model and its nonlinearbehavior [1].

As well, the slip frequency can be calculated as:

dsr

qsrqs

rr

rmsl iL

iRi

LRL

(3)

It is found that the ideal decoupling can beachieved if the above slip angular speed command is used for making field-orientation. For a constant rotor

flux r and 0dt

d r Substituting in equation (2)

yields the rotor flux set as

The vector control or field oriented control (FOC)theory is the base of a special control method for induction motor drives. With this theory inductionmotors can be controlled like a separately excited dcmotor. This method enables the control of field andtorque of the induction machine independently(decoupling) by manipulating the corresponding fieldoriented quantities [1, 2].

dsmr iL (4)

The motor developed torque is directly related to

as follows:*

qsiIn this paper, the configuration and design of thefuzzy logic controller for indirect vector based controlof induction motor has been investigated. Theproposed fuzzy logic controller (FLC) has beensuccessfully simulated on a simulink model with thehelp of fuzzy logic toolbox. The performance of theFLC has been successfully compared with the conventional PI controller. It is found that theproposed FLC is insensitive to load variation andsudden changes in the speed command.

**

4

3qsdr

r

me i

LL

dtdT then T **

qste iK

*

*

3

4

r

e

m

rqs

TLL

Pi (5)

___________________________________________0-7803-8560-8/04/$20.00©2004IEEE

1

3. FUZZY LOGIC SPEED CONTROLLER

PRINCIPLE AND DESIGN

Basically, the fuzzy logic controller consists of fourblocks as shown in Figure 1, Fuzzification, fuzzyinferencing engine, Knowledge base and adefuzzification block.

3.1 Input/output variables

The design starts with assigning the mapped variablesinputs/output of the FLC in Figure 2. The I/O must beclearly defined. In this case the first input variable is the speed error “e” and the second is the change in speed error “ce”=e* at a sampling time “ts”. The twoinput variables e(ts) and ce(ts) are calculated at everysampling time as :

e(ts) = r* (ts) – r(ts) (6)

ce(ts) = e(ts) – e(ts – 1) (7)

Where “ce” denotes the change of e, r (ts) is theactual rotor speed, r

*(ts) is the reference speed ande (ts – 1) is the value of error at a previous samplingtime.

The output variable of the FLC is the change intorque, T (Figure 2), which is integrated (in discretesense) to get the reference torque T*(ts) as shown inthe equation:

Te*(ts) = T*(ts – 1) + T* (8)

3.2 Fuzzification

The success of this work, and the like, depends on how good this stage is conducted. In this stage thecrisp variables of the inputs e(ts) and ce(ts) are converted into fuzzy variables that can be identifiedby the levels of membership in the fuzzy set. Each fuzzy variable is a member of the subsets with adegree of membership μ varying between 0 (non-member) to 1 (full member).

The fuzzy sets are defined as Z=Zero,PS=Positive Small, PM=Positive Medium,PB=Positive Big, NS=Negative Small, NM=NegativeMedium, NB=Negative Big PVS=Positive Very

Small, NVS=Negative V. Small, NVB= Negativevery Big, and PVB= Positive very Big.

The universe of discourse of all the variables,covering the whole region, is expressed in per unitvalues. All the MFs have asymmetrical shape withmore crowding near the origin (steady state). Thispermits higher precision at steady state [1-3].

3.3 Knowledge base and inferencing stage

U

edtd

G3

G2

G1

Main Block of FLC

RB

D

U=G3D

Fuzz

ific

atio

n

G2.e*

e*

Def

uzz

ific

atio

nFS

FISEngine

eG1.e

Knowledge base involves defining the rulesrepresented as IF-THEN rules statements governingthe relationship between inputs and output variablesin terms of membership functions. In this stage theinput variables e(ts) and ce(ts) are processed by the

inference engine that executes 7x7 rules represented

in rule table. Inferencing stage includes also,application of fuzzy operator (AND, OR), implicationand aggregation. An example of rule statementsdescribing the expert system is:

Fig. 1: Complete Fuzzy Logic Controller Used

for Vector Induction Motor ControlIF e(pu) (speed error in per unit) = Z (zero) ANDce(pu) = PS (positive small) THEN du(pu) = PS

(positive)

3.4 Defuzzification stage

This stage introduces different inference methods thatcan be used to produce the fuzzy set value for theoutput fuzzy variable T. In this paper, the center ofgravity (COA) or centroids method is used tocalculate the final fuzzy value T*(ts).

Defuzzification using COA method means thatthe crisp output of T*(ts) is obtained by using thecenter of gravity, in which the crisp du(pu)0 or T(ts)variable is taken to be the geometric center of theoutput fuzzy variable value μout( T) area, whereμout( T) is formed by taking the union of all thecontributions of rules with the degree of fulfillmentgreater than 0. Then the COA expression with a discretized universe of discourse can be written asfollows:

n

iiout

n

iiouti

T

TTT

1

1*(9)

Then by integration Te* is obtained as shown by

equation (8). This Torque value is used to calculateiqs

*, which in turn used to command the inductionmotor via 2 -3 block.

r

*e

m

r*qs

T.

L

L.

P

2.

3

2i (10)

The overall system is shown in Figure 2 (thespecification parameters of the motor are given in the appendix) and the constructed Fuzzy Logic Controllerin MATLAB/SIMULINK environment [4] is shownin Figure 3. The block diagram of the driverepresenting the IVCIM with Fuzzy Logic Control isshown in Figure 4.

2

Ids* Calculation

Fig. 2: Indirect Vector Control Based Induction Motor Block Diagram with Fuzzy Logic Control

4. SIMULATION RESULTS, DISCUSSION AND

COMPARISON

Input1 (speed error)7 MFs

Input2 (change speed error)7 MFs Various simulation tests were carried out on both the PI

controller and the FL controller on the indirect vectorcontrol of induction motor (IVCIM). Time responseand steady state error were compared.

Figures 5 and 6 show the PI and FLC response speedat no load. FLC performed better with respect to risetime and steady state errors.

Output (change in o/p control du)7 MFs Figure 7 shows the speed track performance test,

when a sudden change in speed reference is applied inthe form of a look-up table.

Figures 8 and 9 examine the load disturbancerejection capabilities of each controller when using a load torque step from 0 to 200 N.m applied at 0.6seconds. The FL controller at that moment returnsquickly to the command speed within (0.1sec) with a maximum drop in speed of 0.7rad/sec. whereas the PI controller was affected by the change on load torqueand sustained a steady state error.

Surface Viewer of the FLC

Fig. 3: FIS system (FLC) layout, membership’sfunctions and surface viewer for inputs/output of the

controller.It is found that the FLC is more robust and follow

the difficult ramp without delay. It was also found thatthe FLC did not show significant changes in its responsedue to load variation, whereas the PI controller wassensitive to changes in load conditions.

r*

+ _

ce

IM

e

Error-e

de

ids*

T*

T*(ts) VC and PWM

inverteriqs

*

Calculi

r

FLC

Fig.4: Fuzzy Speed Controller in vector-controlled drivesystem

Fig.5 Speed Response comparison at no-load

3

Fig 6 Enlarged response comparison

Fig 7 Speed tracking response comparison

Fig 8 Speed Response Comparison during Sudden LoadChange

Fig 9 Enlarged results of Fig. 8.

5. CONCLUSION

An indirect vector controlled induction motor drivesystem has been introduced. The drive system wassimulated with both a fuzzy logic controller and aconventional PI, and their performances were compared.Simulation results showed that the fuzzy logic controlleris more robust during load changes and eliminates thetransients during sudden changes in speed. Overallsimulation results showed that the fuzzy controller hashigher performance than the PI controller.

Appendix : Motor specification

Machine Type: 3-phase Induction MotorRotor Type: Squirrel Cage Stator and Rotor: Y-connection to an internal neutral

pointReference Frame: Stationary 50 hp, 1500rpm, (120 rad/sec), 460V 60Hz 4polesRs = 0.087 Rr = 0.228 Ls= 0.8mH Lr = 0.8mHLm = 34.7mH Jn = 1.662Kg.m2 f = 0.1N.m.s

6. REFERENCES

[1] B. K. Bose. Modern Power Electronics and ACDrives, Prentice-Hill PTR Companies, Inc. UpperSaddle River, NJ 07458, 2002.

[2] Hoang Le-Huy, Minh Ta-Cao and J.L. Silva“Fuzzy Logic Based Controller for InductionMotor Drives” Canadian Conference on Electricaland Computer Engineering, 1996., Volume: 2 , 26-29 May 1996

[3] M.N. Uddin, T. S. Radwan and M. A. Rahman“Performance of Novel Fuzzy Logic Based Indirect Vector Control for Induction MotorDrive” Proceedings of IEEE 2000 ref, 0-7803-6401-5.

[4] http://www.mathworks.com (The official site forMATLAB &SIMULINK as well the Fuzzy Logic Toolbox).

4